I have a value stored in x and I need to compare it to the numbers in every other line of a file. The file contains alternating lines of numbers and letters:

aaaa1111
AAAAAAAA
bbbb2222
BBBBBBBB
cccc3333
CCCCCCCC

I need to compare x to the numbers in every other line without the first four characters of that line. So I want to compare x to 1111, then to 2222, then 3333. This is to be the condition in an if statement:

if [ $x = (line 1 without first four characters) ]
or
if [ $x = (line 3 without first four characters) ]

I know I would have to use something along the lines of = $(sed something) or maybe cut, but I don't know how to reference the file by line.